# Calories Burned by Heart Rate Calculator

> Estimates energy expenditure during aerobic exercise from average heart rate, sex, age and weight (optionally VO2max) with the regression equations of Keytel et al. (2005), reporting calories per minute, per hour and for the whole session.

- Calculator id: `calories-by-heart-rate` · Category: Sports & Fitness (`fitness`) · Tool name: `estimate_calories_from_heart_rate`
- Canonical page: https://tttkmbb.com/fitness/calories-by-heart-rate · This document: https://tttkmbb.com/fitness/calories-by-heart-rate.md · JSON definition: https://tttkmbb.com/fitness/calories-by-heart-rate.json

## Purpose

Estimates energy expenditure during aerobic exercise from average heart rate, sex, age and weight (optionally VO2max) with the regression equations of Keytel et al. (2005), reporting calories per minute, per hour and for the whole session.

**Use when:** You have an average heart rate from a monitor for a steady aerobic session and want a calorie estimate, with or without a known VO2max.

**Do not use when:** You know the activity and want a MET-based estimate (use calories-burned), the session was intervals or strength work or outside the 90–150 bpm steady-state range, or the person takes heart-rate-altering medication; informational only.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `sex` | enum: male \| female |  | required | Sex category used to select the formula coefficients. |
| `age_years` | number | years | required | Age in years (the equations were fitted on adults). (min 10, max 100) |
| `weight_kg` | number | kg | required | Body weight in kilograms. (> 0, max 300) |
| `average_heart_rate_bpm` | number | bpm | required | Average heart rate over the session (valid range about 90–150 bpm). (min 60, max 220) |
| `duration_minutes` | number | min | required | Exercise duration in minutes. (> 0, max 1440) |
| `vo2max_ml_kg_min` | number | ml/kg/min | optional | Optional measured or estimated VO2max; when given, the more accurate VO2max-inclusive equation is used. (min 10, max 100) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `calories_burned` | number | kcal | Energy expenditure for the whole session. |
| `calories_per_minute` | number | kcal/min | Energy expenditure rate from the Keytel equation (kJ/min ÷ 4.184). |
| `calories_per_hour` | number | kcal/h | calories_per_minute × 60. |
| `kj_per_minute` | number | kJ/min | The raw Keytel regression value in kilojoules per minute. |
| `method_used` | string |  | Which Keytel equation (sex, with or without VO2max) was applied. |
| `validity_note` | string |  | Whether the heart rate lies in the 90–150 bpm range the equations were derived for. |

## Formula

`Without VO2max: male kcal/min = (−55.0969 + 0.6309·HR + 0.1988·weight_kg + 0.2017·age_years) / 4.184; female = (−20.4022 + 0.4472·HR − 0.1263·weight_kg + 0.074·age_years) / 4.184. With VO2max: male = (−95.7735 + 0.634·HR + 0.404·VO2max + 0.394·weight_kg + 0.271·age_years) / 4.184; female = (−59.3954 + 0.45·HR + 0.380·VO2max + 0.103·weight_kg + 0.274·age_years) / 4.184. calories_burned = kcal/min × duration_minutes`

Keytel et al. (2005) fitted these linear equations to indirect-calorimetry energy expenditure of adults during steady-state treadmill and cycle exercise; the VO2max version is the more accurate of the two. They apply to steady aerobic work at roughly 90–150 bpm and can give unrealistic (even negative) values outside that range. Informational only.

## Data Sources

- Keytel LR et al. (2005) Prediction of energy expenditure from heart rate monitoring during submaximal exercise, J Sports Sci 23:289-297 — https://pubmed.ncbi.nlm.nih.gov/15966347/ (peer_reviewed, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/calories-by-heart-rate?sex=…&age_years=…&weight_kg=…&average_heart_rate_bpm=…&duration_minutes=…`
- `POST https://tttkmbb.com/api/v1/calculate/calories-by-heart-rate` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/calories-by-heart-rate · OpenAPI operationId `estimate_calories_from_heart_rate` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "calories-by-heart-rate", "inputs": {…}}`

## Example

- Male, 30 y, 80 kg, 150 bpm, 45 min: inputs `{"sex":"male","age_years":30,"weight_kg":80,"average_heart_rate_bpm":150,"duration_minutes":45}` → `{"calories_per_minute":14.7,"calories_burned":661.4,"calories_per_hour":881.8,"method_used":"Keytel et al. 2005, male, without VO2max"}`
- Female, 40 y, 62 kg, 135 bpm, 30 min, VO2max 40: inputs `{"sex":"female","age_years":40,"weight_kg":62,"average_heart_rate_bpm":135,"duration_minutes":30,"vo2max_ml_kg_min":40}` → `{"calories_per_minute":8.1,"calories_burned":243.1,"method_used":"Keytel et al. 2005, female, with VO2max"}`

```
GET https://tttkmbb.com/api/v1/calculate/calories-by-heart-rate?sex=male&age_years=30&weight_kg=80&average_heart_rate_bpm=150&duration_minutes=45
```

## Limitations

You know the activity and want a MET-based estimate (use calories-burned), the session was intervals or strength work or outside the 90–150 bpm steady-state range, or the person takes heart-rate-altering medication; informational only. Keytel et al. (2005) fitted these linear equations to indirect-calorimetry energy expenditure of adults during steady-state treadmill and cycle exercise; the VO2max version is the more accurate of the two. They apply to steady aerobic work at roughly 90–150 bpm and can give unrealistic (even negative) values outside that range. Informational only. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How accurate is a heart-rate calorie estimate?**

Individual error is typically ±15–20 %: heart rate also responds to heat, dehydration, caffeine and stress, and fitness changes the heart-rate/oxygen relationship (which is why supplying VO2max improves the estimate).

**Can I use it for weight training or intervals?**

No. Heart rate stays elevated between efforts without matching oxygen use, so the equations over-estimate for intermittent work.

**Does this include resting metabolism?**

Yes: the regression predicts gross expenditure, so subtract about 1–1.3 kcal/min if you want the extra calories above rest.

## Related

- [Calories Burned Calculator](https://tttkmbb.com/fitness/calories-burned.md) — MET-based estimate when the activity is known.
- [Heart Rate Zone Calculator](https://tttkmbb.com/health/heart-rate-zones.md) — Training zones for the same heart rates.
- [VO2 Max Calculator](https://tttkmbb.com/fitness/vo2-max.md) — Estimate the VO2max that improves this calculation.